M-6A. A cord is wrapped around spool of inner and outer radii r and R respective

Question

M-6A. A cord is wrapped around spool of inner and outer radii r and R respectively. The spool of mass m and radius of gyration rests on a flat rough horizontal surface and does not slip whenever it is in rolling motion. Force F is applied to the cord inclined by angle to the surface. Derive formula for resulting horizontal acceleration of the spool?s mass center. Explain in words meaning of positive and negative values of .

M-6B. Planetary mechanism consists of three gears each of mass M and radius r and arm OA which may be regarded as a uniform bar of mass m.The gear 1 is fixed whereas gears 2 and 3 may be regarded as uniform solid disks. Find kinetic energy T of the whole system for the case where the arm rotates in horizontal plane with constant angular velocity .

Ans.

M-6 C. A gymnast A and a weight B - each of mass M ? are attached to a cord/pulley set as shown. The whole system is originally at equilibrium. Then the gymnast starts climbing along the cord with velocityrelative to the cord. What will be the resulting velocity of the cord with attached weight B if the pulley may be regarded as a thin solid disk of mass m and outer radius R? You may obtain the solution using conservation of angular momentum principle.

M- 6 D. A right triangular prism ABD with inclination angle and mass m can slide without friction along smooth horizontal surface. A uniform solid cylinder of mass m rolls down the inclined surface AB without friction. If both cylinder and prism are at rest initially, what will be the relative velocity and absolute velocity of the cylinder?s center O after its height decreased by h. Ans. ,

Hints: 1. You may use conservation of momentum principle for the system cylinder-prism to relate velocities of prism and of cylinder?s center (absolute and relative )

2. When you apply conservation of energy relation do NOT forget to account for kinetic energy of the cylinder?s rotation.

Solutions are to be brought in at the Exam # 4, by 9:50 AM on10/11/12.

Fig. M-6A

Fig. M-6B

Fig. M-6C

M-6A. A cord is wrapped around spool of inner and outer radii r and R respectively. The spool of mass m and radius of gyration M-6A. A cord is wrapped around spool of inner and rests on a flat rough horizontal surface and does not slip whenever it is in rolling motion. Force F is applied to the cord inclined by angle M-6A. A cord is wrapped around spool of inner and to the surface. Derive formula for resulting horizontal acceleration M-6A. A cord is wrapped around spool of inner and of the spool?s mass center. Explain in words meaning of positive and negative values of M-6A. A cord is wrapped around spool of inner and . M-6B. Planetary mechanism consists of three gears each of mass M and radius r and arm OA which may be regarded as a uniform bar of mass m.The gear 1 is fixed whereas gears 2 and 3 may be regarded as uniform solid disks. Find kinetic energy T of the whole system for the case where the arm rotates in horizontal plane with constant angular velocityM-6A. A cord is wrapped around spool of inner and . Ans. M-6A. A cord is wrapped around spool of inner and M-6 C. A gymnast A and a weight B - each of mass M ? are attached to a cord/pulley set as shown. The whole system is originally at equilibrium. Then the gymnast starts climbing along the cord with velocityM-6A. A cord is wrapped around spool of inner and relative to the cord. What will be the resulting velocity M-6A. A cord is wrapped around spool of inner and of the cord with attached weight B if the pulley may be regarded as a thin solid disk of mass m and outer radius R? You may obtain the solution using conservation of angular momentum principle. M- 6 D. A right triangular prism ABD with inclination angle M-6A. A cord is wrapped around spool of inner and and mass m can slide without friction along smooth horizontal surface. A uniform solid cylinder of mass m rolls down the inclined surface AB without friction. If both cylinder and prism are at rest initially, what will be the relative velocityM-6A. A cord is wrapped around spool of inner and and absolute velocity M-6A. A cord is wrapped around spool of inner and of the cylinder?s center O after its height decreased by h. Ans. M-6A. A cord is wrapped around spool of inner and ,M-6A. A cord is wrapped around spool of inner and Hints: 1. You may use conservation of momentum principle for the system cylinder-prism to relate velocities of prism and of cylinder?s center (absolute M-6A. A cord is wrapped around spool of inner and and relativeM-6A. A cord is wrapped around spool of inner and ) 2. When you apply conservation of energy relation do NOT forget to account for kinetic energy of the cylinder?s rotation. Solutions are to be brought in at the Exam # 4, by 9:50 AM on10/11/12. M-6A. A cord is wrapped around spool of inner and Fig. M-6A M-6A. A cord is wrapped around spool of inner and Fig. M-6B M-6A. A cord is wrapped around spool of inner and Fig. M-6C M-6A. A cord is wrapped around spool of inner and

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